Should I replace this cap? [solved]

If the other 680 is reading fine that 680 is probably open. One thing that is important is to measure with the probe tips touching the actual leads of the resistor, not the terminals it is soldered to. That way the measurement can't be affected by a bad connection to the terminal. If that doesn't bring any new info to light, the most sure way to verify the resistor's value is to disconnect one end from the circuit so it can't be affected by caps charging or other components' resistance.
 
So I removed that 680 Ohm resistor between 26 and 31, and sure enough, it was open!

When I now measure resistance across terminals 26 and 31 (in the absence of the resistor) it charges like a cap, just like before when the broken resistor was in place, so I assume the capacitance is some sort of circuit property that reveals itself when the resistor is blown or removed. I will call the Queen today for a replacement. If there is anything you think I should check before replacing the resistor, please let me know. Will report back when I install the new 680. Thanks so much Paul and Doc - you guy are amazing!
 
Yes if the relatively low value 680 ohm resistor is functional it will effectively shunt any charge buildup across a large value cap that is in parallel in the circuit, and thus you won't see much charging behavior in the ohm meter. Once that resistor opens up, the cap will exhibit that typical "rising ohms" characteristic when the meter battery tries to charge it.
 
I just wanted to thank everyone again for their help with this problem - I replaced the resistor, and the diagnosis was correct! Voltages all dead on, and really great music from both channels. Thanks so much for the help - you guys really are the best and make this hobby a ton of fun.
 
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